Question: Simplify; express your answer in exponential form. Assume $p\neq 0, y\neq 0$. $\dfrac{{(p^{2})^{-5}}}{{(p^{3}y^{-5})^{2}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{2}}$ to the exponent ${-5}$ . Now ${2 \times -5 = -10}$ , so ${(p^{2})^{-5} = p^{-10}}$ In the denominator, we can use the distributive property of exponents. ${(p^{3}y^{-5})^{2} = (p^{3})^{2}(y^{-5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{2})^{-5}}}{{(p^{3}y^{-5})^{2}}} = \dfrac{{p^{-10}}}{{p^{6}y^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-10}}}{{p^{6}y^{-10}}} = \dfrac{{p^{-10}}}{{p^{6}}} \cdot \dfrac{{1}}{{y^{-10}}} = p^{{-10} - {6}} \cdot y^{- {(-10)}} = p^{-16}y^{10}$.